The Journal of Online Mathematics and Its Applications, Volume 7 (2007)
Bouncing Balls and Geometric Series, Robert Styer and Morgan Besson

The Question

Introductory Video.

In this video, a ping-pong ball is dropped on a table. The ball seems to stop bouncing after a matter of seconds. But suppose the ball bounces infinitely often, and suppose we could detect the tiniest micro-bounces. When would the ball stop bouncing?